Heavy quarkonia (bound state of \(c\bar{c}\)  and \(b\bar{b}\) )
is a very promising signature
of the hot and dense quark matter produced at the
heavy ion collision experiments at RHIC and LHC. In non-central
collisions, a very strong magnetic field (around \(m_{\pi }^2-15 m_{\pi }^2\) ) is
also generated whose life time is elongated by
the electrical conductivity of the medium. In addition to this a large quark
chemical potential (100-200 MeV) is also
present near the deconfinement region
 [1]}, [2]}.
The influence of the strong magnetic field on the
properties of the heavy quarkonia immersed in hot QCD medium have
been studied
in recent years by two of us in strong
 [3]}, [4]} as well as
in weak magnetic field [5]}. In other
works the effect of the magnetic field has been
investigated for the case of a harmonic interaction
and for Cornell potential plus a spin spin interaction term
in [6]}, [7]} and
using the generalized Gauss law in [8]}.
In present work, we have
explored the effects of finite \(\mu \)  on the
\(Q\bar{Q}\)  bound states immersed in strongly magnetized
hot QCD medium. In order to incorporate the non-perturbative
part we have added a phenomenological term induced by dimension
two gluon condensate in gluon
propagator in addition to usual HTL resummed propagator.
